Conventional mixer technology relies on the nonlinear, or square-law, behavior of a semiconductor junction device (diode) to achieve translation of a bandpass modulation signal from one carrier frequency to another. For example, to perform frequency conversion in a conventional radio frequency (RF) diode-based mixer, two excitation signals are used to bias a diode or network of diodes: the local oscillator (LO) signal and the RF signal. The LO signal is typically a continuous-wave (CW) signal, while the RF signal is often a complex bandpass modulated signal. The goal of basic frequency conversion is to preserve the RF signal modulation content, but shift it spectrally to a new intermediate frequency (IF) carrier frequency.
The CW RF signal cos(ωRFt) and CW LO signal cos(ωLOt) can be used as the AC portion of a diode bias signal v(t) to form v(t)=(vrf cos ωrft′vlo cos ωlot) where vrf is the RF signal AC intensity, vlo is LO signal AC intensity, ωrf is the RF radian frequency, and ωlo is the LO radian frequency. The resulting current through the diode, I(v), may be expressed mathematically as a Taylor series. The equation below shows the first three terms in the series:
      I    ⁡          (      υ      )        =                    G        d        ′            2        ⁢          (                        υ          rf          2                +                  υ          lo          2                +                              υ            rf            2                    ⁢          cos          ⁢                                          ⁢          2          ⁢                                          ⁢                      ω            rf                    ⁢          t                +                              υ            lo            2                    ⁢          cos          ⁢                                          ⁢          2          ⁢                                          ⁢                      ω            lo                    ⁢          t                +                  2          ⁢                                          ⁢                      υ            rf                    ⁢                      υ            lo                    ⁢                      cos            ⁡                          (                                                ω                  rf                                -                                  ω                  lo                                            )                                ⁢          t                +                  2          ⁢                                          ⁢                      υ            rf                    ⁢                      υ            lo                    ⁢                      cos            ⁡                          (                                                ω                  rf                                +                                  ω                  lo                                            )                                ⁢          t                    )      
This equation indicates that the two input sinusiod signals (RF and LO) result in several output sinusiod signals at a variety of carrier frequencies. The equation indicates responses at DC, at twice each individual signal carrier frequency, and at the sum and difference frequencies. The conversion frequency ωc is defined as ωc=(ωrf−ωlo) or (ωrf+ωlo). This means that two different RF input frequencies can result in the same output frequency, a limitation of conventional mixer technology.
In general, the mixer output is filtered such that all signal terms except the one at ωc is greatly attenuated. The selected ωc term is often referred to as the intermediate frequency (IF) term. Practically, attenuation of undesired terms due to filtering is finite, and potentially problematic signal content related to higher-order Taylor series terms is also present at the mixer output.